Lévy Processes and Stochastic Calculus ICM Edition (Cambridge Studies in Advanced Mathematics, Series Number 116)

Applebaum, David

ISBN 10: 0521170117 / ISBN 13: 9780521170116

Published by Cambridge University Press, 2010

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Bibliographic Details

• Title: Lévy Processes and Stochastic Calculus ICM Edition (Cambridge Studies in Advanced Mathematics, Series Number 116)
• Publisher: Cambridge University Press
• Publication Date: 2010
• Language: English
• ISBN 10: 0521170117
• ISBN 13: 9780521170116
• Binding: Soft cover
• Edition: 2nd Edition
• Condition: New

About this title

Synopsis

Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Levy processes, then leading on to develop the stochastic calculus for Levy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Levy processes to have finite moments; characterization of Levy processes with finite variation; Kunita s estimates for moments of Levy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Levy processes; multiple Wiener-Levy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Levy-driven SDEs.

Book Description

A unique development of these two subjects contained in a single volume. New topics featured in this fully revised edition include regular variation and subexponential distributions, characterisation of Lévy processes with finite variation, multiple Wiener-Lévy integrals and chaos decomposition, and introductions to Malliavin calculus and stability theory for Lévy-driven SDEs.